Question

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.4 inches, and standard deviation of 7.9 inches. A) What is the probability that a randomly chosen child has a height of less than 64.95 inches? Answer= (Round your answer to 3 decimal places.) B) What is the probability that a randomly chosen child has a height of more than 49.8 inches? Answer= (Round your answer to 3 decimal places.) Submit Question

Answer 1

Solution :

Given that,

mean = = 56.4

standard deviation = = 7.9

A ) P( x < 64.95 )

P ( x - / ) < ( 64.95 - 56.4 / 7.9)

P ( z < 8.55 /7.9 )

P ( z < 1.08)

= 0.8599

Probability = 0.860

B ) P (x > 49.8 )

= 1 - P (x < 49.8 )

= 1 - P ( x -  / ) < ( 49.8 - 56.4 / 7.9)

= 1 - P ( z < -6.6 / 7.9 )

= 1 - P ( z < -0.83)

Using z table

= 1 - 0.2033

= 0.7967

Probability = 0.797